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Topic: Markov chain


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In the News (Tue 10 Nov 09)

  
  [Markov Chains] model, script, tool, decision process [Markov Chains]
With a Markov chain, it is not necessary to have a certain number of starting parameters to obtain a final parameter.
I have now explained to you what a Markov chain is, or at least I have explained them to you from the point of view of random text production.
Markov Chains are a statistical method that analyze the relationship between adjacent words in a text.
en.kerouac3001.com /markov-chains-spam-that-search-engines-like-pt-1-5.htm   (0 words)

  
  Markov chain - MLpedia
Markov chains are related to Brownian motion and the ergodic hypothesis, two topics in physics which were important in the early years of the twentieth century, but Markov appears to have pursued this out of a mathematical motivation, namely the extension of the law of large numbers to dependent events.
Markov chains also have many applications in biological modelling, particularly population processes, which are useful in modelling processes that are (at least) analogous to biological populations.
That is, Markov chains are used in two to three dimensional stochastic simulations of discrete variables conditional on observed data.
www.mlpedia.org /index.php?title=Markov_chain   (1498 words)

  
  Markov chain Summary   (Site not responding. Last check: )
Markov chains are often described by a directed graph, where the edges are labeled by the probabilities of going from one state to the other states.
Markov chains also have many applications in biological modelling, particularly population processes, which are useful in modelling processes that are (at least) analogous to biological populations.
Markov chains are related to Brownian motion and the ergodic hypothesis, two topics in physics which were important in the early years of the twentieth century, but Markov appears to have pursued this out of a mathematical motivation, namely the extension of the law of large numbers to dependent events.
www.bookrags.com /Markov_chain   (2434 words)

  
 PlanetMath: Markov chain
That is, the next value of the chain depends only on the current value, not any previous values.
Markov chains are arguably the simplest examples of random processes.
This is version 2 of Markov chain, born on 2002-04-29, modified 2006-12-31.
planetmath.org /encyclopedia/MarkovChain2.html   (140 words)

  
 Markov Explanation
A Markov analysis looks at a sequence of events, and analyzes the tendency of one event to be followed by another.
A Markov Chain, while similar to the source in the small, is often nonsensical in the large.
Markov processes have been used to generate music as early as the 1950's by Harry F. Olson at Bell Labs.
www.doctornerve.org /nerve/pages/interact/markhelp.htm   (731 words)

  
 MARKOV CHAIN   (Site not responding. Last check: )
It is named after A. Markov who at the turn of the century studied poetry and other texts as stochastic sequences of characters (symbols, letters, syllables, and words).
The probabilities of a Markov chain are usually entered into a transition matrix indicating which state or symbol follows which other state or symbol.
The order (see ordinality) of a Markov chain corresponds to the number of states or symbols from which probabilities are defined to a successor.
pespmc1.vub.ac.be /ASC/Markov_chain.html   (130 words)

  
 Markov Chains
A Markov chain, named in honor of Russian mathematician Andrei Markov, is a stochastic process.
The interesting thing about this chain is that when d is large and when the Markov chain runs for a long time, there would most likely be approximately d/2 balls in Urn 1.
Markov chains also have many biological applications, particularly population processes, which are useful in modelling processes that are, at least, analogous to biological populations.
cs.bilgi.edu.tr /~bulent/MarkovChains.html   (1400 words)

  
 Baseball as a Markov Chain
The concept of a Markov chain is not new, dating back to 1907, nor is the idea of applying it to baseball, which appeared in mathematical literature as early as 1960.
However, formal Markov chain analysis of baseball is not at all common and is rarely found outside of academic studies.
The heart of the Markov chain is the analysis of the transitions between the states.
www.pankin.com /markov/intro.htm   (3716 words)

  
 Digital Music Programming II: Markov Chains
A second-order Markov chain would mean that the current state and the last state affect the choice of the next event.
A third-order Markov chain would indicate that the current state and the last two states in the sequence will affect the choice of the next state.
Analysis and Synthesis of Palestrina-Style Counterpoint Using Markov Chains by Mary Farbood and Bernd Schoner.
peabody.sapp.org /class/dmp2/lab/markov1   (914 words)

  
 Hidden Markov Model
This chain of states and the transitions between them is reminiscent of the Markov Chain and still more of this offspring, the hidden Markov model.
Compared to Markov Chain, the output sequences generated by an HMM are what is known as doubly stochastic: not only is the transitioning from one state to another stochastic (probabilistic), but so is the output symbol generated at each state.
The Markov nature of the an HMM (namely, that the probability of being in a state is dependent only on the previous state) admits use of the Viterbi algorithm, most likely to have generated the given sequence of symbols, without having to search all possible sequences.
project.uet.itgo.com /markov_model.htm   (1783 words)

  
 SOKOL -- AN INTUITIVE MARKOV CHAIN LESSON FROM BASEBALL   (Site not responding. Last check: )
We have found that it is helpful to have students analyze a Markov chain application (i) that is easily explained, (ii) that they have a familiar understanding of, (iii) for which a large amount of real data is readily available, and (iv) that teaches them new insights about the application they thought was so familiar.
The Markov chain is used to model the progression of a half-inning of baseball, in which one team bats until three outs have been made.
Thinking about whether the Markov chain exactly models the underlying process is important, but equally important from an educational standpoint is reinforcing the idea that a model can be appropriate for use even though it is not exact.
ite.pubs.informs.org /Vol5No1/Sokol/index.php   (3934 words)

  
 Web Site for Perfectly Random Sampling with Markov Chains:
One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution.
The initial states of the Markov chains are chosen at random, and if the probability of rejection in rejection sampling is known, then rigorous estimates of the mixing time are given.
The Markov chain of interest is lifted to one that keeps track of 1) the original chain's state, and 2) the number of steps since the original chain's state took on that special value.
dbwilson.com /exact   (14686 words)

  
 MARCA: MARkov Chain Analyzer.
MARCA is a software package designed to facilitate the generation of large Markov chain models, to determine mathematical properties of the chain, to compute its stationary probability, and to compute transient distributions and mean time to absorption from arbitrary starting states.
The ``embedded'' Markov chain may be analyzed to determine its periodicity, When this is greater than 1, an option is available to permute the transition matrix into normal cyclic form.
The evolution of the Markov chain is represented by the movement of balls among the buckets.
www.csc.ncsu.edu /faculty/stewart/MARCA/marca.html   (1254 words)

  
 Lower Order Markov Chains
Markov Chains are being covered by another project in this course therefore I will be brief as to the covering the Markov chains in this section, and how they can be useful for image analysis Why would we want to use Markov chains in pattern recognition.
Markov chains have the property that given the present condition of the pixel we are examining, the state of the next pixel is conditionally independent of the pixel that is currently being examined.
A set of pixels can be thought of as such a chain where the probability of the state of a pixel being 1 or 0 is dependent on the states of the two pixels around it.
www.bic.mni.mcgill.ca /~mallar/CS-644B/markovchains.html   (1140 words)

  
 Markov chain
A sequence of random variables in which the future variable is determined by the present variable but is independent of the way in which the present state arose from its predecessors.
In other words, a Markov chain describes a chance process in which the future state can be predicted from its present state as accurately as if its entire earlier history was known.
Markov chains are named after the Russian mathematician Andrei Andrevich Markov (1856-1922) who first studied them in a literary context, applying the idea to an analysis of vowels and consonants in a text by Pushkin.
www.daviddarling.info /encyclopedia/M/Markov_chain.html   (189 words)

  
 Markov chains
A Markov chain is a sequence of random values whose probabilities at a time interval depends upon the value of the number at the previous time.
The controlling factor in a Markov chain is the transition probability, it is a conditional probabilty for the system to go to a particular new state, given the current state of the system.
Markov chains can be used to solve a very useful class of problems in a rather remarkable way.
www.taygeta.com /rwalks/node7.html   (686 words)

  
 Markov Chains in Theoretical Computer Science, Spring 2002   (Site not responding. Last check: )
Definition of the chain, analysis that it converges rapidly for large enough $k$, algorithm for approximating the number of $k-$colorings of a graph.
Eigenvectors, the symmetric version of a Markov chain, the connection between spectral gap and rapid mixing, expansion, expanders, using expanders to reduce the number of random bits used to amplify probability of a BPP algorithm, The notion of conductance of a graph.
Canonical paths defined, simple examples, chain on all matchings in a graph with weight proportional to number of edges in matchings; Proof that is converges in time polynomial is lambda, 1/epsilon and n.
www.cs.huji.ac.il /~doria/markovchains.huji2002.html   (1457 words)

  
 Mathematics of Markov Chain Monte Carlo
Mathematics of Markov Chain Monte Carlo was held from Monday, June 12 through Friday, June 16 at the Mathematical Sciences Research Institute in Berkeley, California.
Markov chains are a class of stochastic processes which (under mild regularity conditions) converge to a unique stationary distribution.
In the spring of 2005, mixing times of finite Markov chains were a major theme of the multidisciplinary research program Probability, Algorithms, and Statistical Physics, held at MSRI.
www.oberlin.edu /markov/workshop.html   (496 words)

  
 Markov Model of Natural Language
Markov chains are now widely used in speech recognition, handwriting recognition, information retrieval, data compression, and spam filtering.
For the purpose of this assignment, a Markov chain is comprised of a set of states, one distinguished state called the start state, and a set of transitions from one state to another.
The full Markov chain for k = 3 is illustrated in the figure from the previous section.
www.cs.princeton.edu /courses/archive/spr05/cos126/assignments/markov.html   (2268 words)

  
 Markov Analysis Software
MKV is a Markov Analysis program for analysing state transition diagrams (markov chain) using numerical integration techniques.
Markov analysis provides a means of analysing the reliability and availability of systems whose components exhibit strong dependencies.
The major drawback of Markov methods is that Markov diagrams for large systems are generally exceedingly large and complicated and difficult to construct.
www.isograph.com /markov.htm   (623 words)

  
 chain: run a Monte Carlo Markov Chain
Before running any chains you must perform a fit.  The MCMC algorithm uses the correlation matrix produced at the end of a fit as the initial source for the proposal distribution.
recalc derives a new proposal distribution from the current chains.  This assumes a multidimensional normal distribution and is described using eigenvectors and eigenvalues which are then stored in the standard xspec arrays.
All loaded chains must contain the same fit parameters.  xspec will prevent the loading of a chain with a different number of parameters from the currently loaded chains.
starchild.gsfc.nasa.gov /xanadu/xspec/manual/XSchain.html   (360 words)

  
 Math 92.653 -- SELECTED TOPICS: Markov Chains   (Site not responding. Last check: )
This is a question about what is known as a Markov chain or a random walk.
Markov chains are a key tool in Statistics, Physics, Computer Science, and Combinatorial counting, among others.
Instead of a final exam, in the final class of the semester each student will be expected to give a 20 minute presentation, with an accompanying 2+ page write-up, on a Markov chain topic of the student's choice.
www.ravimontenegro.com /markov   (705 words)

  
 Markov Baseball Models Theory
A Markov chain is a mathematical model that can be thought of a being in exactly one of a number of states at any time.
The Markov chain assumption means that we don't care how we arrived at a particular situation.
The key output of the Markov chain baseball model is the computation of the expected runs in the remainder of the inning after any runners and outs state.
www.pankin.com /markov/theory.htm   (2854 words)

  
 markov text   (Site not responding. Last check: )
One of the things about a Markov chain algorithm is that it treats punctuation as part of a word.
Markov algorithms have often been used to produce texts that are both nonsensical and rather plausible.
For this reason Markov processes are called 'finite state machines': each state is determined by the one previous.
www.in-vacua.com /markov_text.html   (825 words)

  
 Markov Chain Monte Carlo
is the lag 1 autocorrelation of the Markov Chain.
Thus, regardless of the chain's current state, the candidate values are always drawn from the exact same distribution.
For the Beta(1,1), the chain does move through the parameter space, but there is a sizable number of repeats.
www.ms.uky.edu /~viele/sta630u02/mcmc/mcmc.html   (2262 words)

  
 Markov Chains
A Markov chain, as I understand it, is a graph that carries probabilities in its edges.
My friend Cassidy Curtis had the great idea of generating two Markov chains from two very different sources (say from two languages) and interpolating between the two graphs, and I wrote a program in Java to do this.
It’s called “A” for historical reasons: the first Markov chain program I wrote 10 years ago was called “a” because I understood the concepts but couldn’t remember the name “Markov”.
www.teamten.com /lawrence/projects/markov   (1060 words)

  
 Software for Flexible Bayesian Modeling and Markov Chain Sampling
This software supports Bayesian regression and classification models based on neural networks and Gaussian processes, and Bayesian density estimation and clustering using mixture models and Dirichlet diffusion trees.
It also supports a variety of Markov chain sampling methods, which may be applied to distributions specified by simple formulas, including simple Bayesian models defined by formulas for the prior and likelihood.
Before trying to use the software, you may need to read various references that describe the models and the Markov chain methods used.
www.cs.toronto.edu /~radford/fbm.software.html   (341 words)

  
 Fastest mixing Markov chain on a graph   (Site not responding. Last check: )
The associated Markov chain has a uniform equilibrium distribution; the rate of convergence to this distribution, i.e., the mixing rate of the Markov chain, is determined by the second largest (in magnitude) eigenvalue of the transition matrix.
For many of the examples considered, the fastest mixing Markov chain is substantially faster than those obtained using these heuristic methods.
We derive the Lagrange dual of the fastest mixing Markov chain problem, which gives a sophisticated method for obtaining (arbitrarily good) bounds on the optimal mixing rate, as well the optimality conditions.
www.stanford.edu /~boyd/fmmc.html   (328 words)

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